Stock gains accelerated late Monday morning amid reports that a new Fed chair nominee will be announced this afternoon and that it might be White House adviser Ben Bernanke, a choice that would be unsurprising -- and therefore reassuring to investors.

The White House said that it will announce its nominee to replace outgoing Federal Reserve Chairman Alan Greenspan later Monday. A source tells CNN the choice will be Bernanke, a former Fed governor.

Bernanke in a prepared text said "I'm thankful for this opportunity but the real test will be if we can get the Dow up above 35,000 before the 2006 Congressional elections. With just the right jaw boning and perhaps a stealth rate cut or two, I think we can rally this puppy to Greenapan type gains."